Image Processing Reference
In-Depth Information
Chapter 2
What Is a Logic-Based Filter?
When a fuzzy fax or faded photocopy is received, it is usually possible to figure out
what it says although the text may be badly damaged or corrupted by noise. This is
because the human brain has knowledge of the characters and fonts of the alphabet
and is able to fill in the gaps (or ignore noise) using experience. Over time, the brain
has learned roughly what to expect and can correct it. The image in Fig. 2.1 is a text
document that has been corrupted with 10% additive noise. This type of corruption
is called salt-and-pepper noise.
It is clear that the document could be typed out again to reproduce the original
version precisely. Therefore it is possible to restore the document fully, using intel-
ligent human intervention. It might be more difficult to do this for unfamiliar alpha-
bets such as Chinese or Arabic if the person had no previous knowledge of the
shapes of the characters.
The important question is this: Is it possible for a computer program to “learn”
this process? The answer is “Yes,” certainly to a very large extent.
Consider the following approaches:
•
Employment of a standard filter such as the median or positive/negative me-
dian;
•
Heuristic approaches for estimating a good filter;
•
The use of statistics to identify the optimal filter out of all filters.
Many image processing specialists will immediately reach for the median filter
on seeing the type of noise present in Fig. 2.1.
1
The median filter takes the pixels
within a small window, places them in rank order and selects the middle one. In this
text document, the image has only two levels, 0 and 1 (or black and white). The me-
dian in this case corresponds to a simple count of the pixels in the window. If more
than half are black, then the output is set to black, otherwise it is set to white. There
are two main disadvantages to this approach. The first is that the median is a
dual
operator
. This means that its effect on black pixels is exactly mirrored by its effect
on white pixels. In this case, we have only additive noise and so the ideal filter
9
